Yes, we can build anything we need, and do it right, if only good managers are employed in both public and private sectors.
If you want examples, the construction of the Oliver Hazard Perry class destroyers at Williamstown dockyards went swimmingly and produced a better finished product than the American original. The Anzac frigate program went reasonably well as far as I can tell.
The problem is that managers with no technical background, let alone never having been on the shop floor themselves, consistently deprecate experience, even to the point of suppressing it by firing workers who know more than they do. I've seen it done regularly. I was even once tempted to do it myself as a manager when I got tired of the "Listen Sonny, that's not the way it's done" remarks.
My guess would be that the foreman, welders and low level planners and clerks who built the Anzac class frigates were "let go' years ago. Consequently, we are way back up the learning curve, and experience must be painfully and expensively reacquired.
On a technical note, building something like this is not just a matter of cutting out plate and welding it together, there is a huge problem in regard to distortion of welded structures which has to be managed by how you support the structure during construction, how you pre-stress various bits and in what order you build and weld. That requires great experience and it doesn't come in text books either.
So to all the new staff at BAe, all I can say is "welcome to the shipbuilding industry'. I just hope you aren't saddled with any English Oxbridge educated managers, they really know how to fcuk things up.
..As for new submarines. Assuming that we haven't "let go" the folk that built the Collins class, I believe that they would produce a better product this time,if allowed to by their managers.
P.S. "Buying off the shelf" has the benefit of nice overseas postings for Officers, complete with nice allowances, etc.